A127680 a(0) = 1; a(n+1) = Sum_{k=0..n} a(n-k)*a(floor(k/2)).
1, 1, 2, 4, 8, 17, 35, 74, 154, 324, 677, 1422, 2977, 6246, 13086, 27444, 57518, 120600, 252794, 529994, 1111013, 2329187, 4882755, 10236280, 21458943, 44986461, 94308415, 197707134, 414469000, 868886834, 1821517772, 3818600772
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
f[l_List] := Block[{n = Length[l] - 1},Append[l, Sum[l[[n - k + 1]]*l[[Floor[k/2] + 1]], {k, 0, n}]]];Nest[f, {1}, 33] (* Ray Chandler, Feb 13 2007 *)
Formula
G.f. A(x) satisfies: A(x) = 1 / (1 - x * (1 + x) * A(x^2)). - Ilya Gutkovskiy, Nov 15 2021
a(n) ~ c * d^n, where d = 2.096382783759695271747034891835844892559952962948180418542044889824924... and c = 0.413348184087944400305975399220165744000861336139702047444087822224828... - Vaclav Kotesovec, Nov 16 2021
Extensions
Extended by Ray Chandler, Feb 13 2007